Question

Ernest Rutherford (the first New Zealander to be awarded the Nobel Prize in Chemistry) demonstrated that nuclei were very small and dense by scattering helium-4 nuclei (⁴He) from gold-197 nuclei (¹⁹⁷Au). The energy of the incoming helium nucleus was 7.39 ✕ 10⁻¹³ J, and the masses of the helium and gold nuclei were 6.68 ✕ 10⁻²⁷ kg and 3.29 ✕ 10⁻²⁵ kg, respectively (note that their mass ratio is 4 to 197). (Assume that the helium nucleus travels in the +x direction before the collision.)

(a)

If a helium nucleus scatters to an angle of 102° during an elastic collision with a gold nucleus, calculate the helium nucleus' final speed (in m/s) and the final velocity (magnitude in m/s and direction counterclockwise from the +x-axis) of the gold nucleus.

⁴He speed m/s?

¹⁹⁷Au velocity m/s?

¹⁹⁷Au direction ° counterclockwise from the +x-axis?

(b)

What is the final kinetic energy (in J) of the helium nucleus?

J?

Answer 1

In this question, there are collision in plane and we need to keep in mind the horizontal as well as vertical components of momentum and apply the law of conservation of momentum and conservation of kinetic energy-